Gura is awkward and probably has regularly dealt with perceived unfairness all her life. This leads her to being a person that desires comfort and dependency on others. She has probably tried making friends but discovers she is not popular at all, but the few friends she has, she is deeply personal and happy with, and this has been her way of making friends. She enjoys personal connection, and invested time to learn and connect further to each other. This feature means making new friends is genuinely hard, as one, the person has to meld with her, and two, she knows that she would want the friendship that means years of investment.
In summary, Gura is eccentric girl who likes deep connections, and sharing her world with, which is a friendship of commitment and time, required by the other party.
Most people who have friends like this, because it was out of control. i.e. school and work, time and location was already chosen, so friends were made, not chosen.
Ame on the other hand, is friendly out the gate. She has little resistance to accepting others and what makes her even more popular is her ability to be a social chameleon and converse with anyone, be they autistic, eccentric, casual, serious, silent, crazy, or angry. She is very well-trained in being able to talk to all kinds, and so is not only popular with everyone, but friends with everone.
Ame is not as beholden to her own eccentricities as Gura is. Gura, in short, has an ego, a sense of self and individuality. This may be due to unfairness and the world not being fair to her.
Not to say Ame doesn't, but the difference is, Ame feels its not important and doesn't believe in ideas of the ego. She doesn't give herself one, nor give other one too. This may be in effort to treat everyone equally.
In summary, Ame and Gura can't work. Gura is needy, and wants Ame to herself. Ame is a free spirit, and doesn't function with Gura's ideas of friendship. She simply finds most of her happy moments with Gura, but she will never grant Gura the credit of being a 'fit' with her, because it was the moment she had, not Gura herself.
Imo, I don't agree with Ame types of personality. They are chill, and fun, no doubt, but discover they only have either family or a few personal friends they have not invested time in, as they chose to spread between 100s of people. I knew a dude just like Ame, and even tho we laughed so hard together, he just had much fun with others. He has had multiple girlfriends and keeps moving through people. Hes massively successful, but I can't help but not relate. Maybe Ame is happy, but my friend drinks and has never kept a relationship and has only his family and has never talked to any of his old friends, and isnt so glad about it.